考虑舵机时滞的阵风减缓主动控制律设计

杨阳; 杨超; 吴志刚; 戴玉婷

doi:10.13700/j.bh.1001-5965.2019.0635

考虑舵机时滞的阵风减缓主动控制律设计

doi: 10.13700/j.bh.1001-5965.2019.0635

北京航空航天大学航空科学与工程学院, 北京 100083

基金项目:

国家自然科学基金 11672018

详细信息

作者简介:
杨阳  男，博士研究生。主要研究方向：气动弹性力学及主动控制

杨超  男，博士，教授，博士生导师。主要研究方向：气动弹性力学与控制

吴志刚  男，博士，副教授，博士生导师。主要研究方向：气动弹性力学与控制

戴玉婷  女，博士，副教授，博士生导师。主要研究方向：气动弹性力学与控制

通讯作者:
吴志刚, E-mail: wuzhigang@buaa.edu.cn

中图分类号: V215.3
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出版历程
- 收稿日期: 2019-12-18
- 录用日期: 2020-01-21
- 网络出版日期: 2020-12-20

Design of gust alleviation active control law considering time-delay of servo actuator

School of Aeronautic Science and Engineering, Beihang University, Beijing 100083, China

Funds:

National Natural Science Foundation of China 11672018

More Information

Corresponding author: WU Zhigang, E-mail: wuzhigang@buaa.edu.cn

摘要

摘要:
针对存在舵机时滞环节的气动伺服弹性系统，提出基于Padé近似和线性二次高斯（LQG）控制的阵风减缓主动控制律设计方法。利用Padé近似将舵机中的时滞环节线性化为一个高阶传递函数并引入气动弹性模型，建立线性的阵风减缓受控模型；利用LQG控制方法对线性化模型设计阵风减缓主动控制系统，并采用平衡截断法对所设计的控制系统进行降阶；利用Simulink将所设计的控制系统引入非线性模型中，得到von Karman连续阵风激励情况下系统的开/闭环响应情况。计算结果表明：根据所提方法设计的阵风减缓主动控制律能有效降低原气动伺服弹性系统的阵风响应，对研究对象机身过载的抑制在15%左右，而对翼根弯矩的抑制达到25%以上。
- 气动伺服弹性 /
- 阵风减缓主动控制 /
- 时间延迟 /
- Padé近似 /
- 最优控制
Abstract:
For the aersevoelastic model including servo actuators with time-delay segment, the design method of gust alleviation control system is proposed based on Padé approximation and Linear Quadratic Gaussian (LQG) control method. Padé approximation was used to linearize the time-delay segment to a high-order transfer function, and then this function was introduced to an aeroelastic model to establish a linear controlled model of gust alleviation. The LQG method was applied to design a gust alleviation control system based on the linear model, and the order of control system was reduced by the balance truncation method. By using Simulink, the designed control system was introduced to the nonlinear model to calculate the gust responses of open/closed systems under von Karman continuous gust model. The results showed that the gust alleviation control system based on the proposed method could effectively reduce the gust responses of the original model with time-delay. The overloads of the airplane were reduced by around 15% and the root bend moment was reduced by more than 25%.
- aeroservoelasticity /
- gust alleviation active control /
- time delay /
- Padé approximation /
- optimal control

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图 1 飞翼布局飞机结构模型及传感器舵机布置

Figure 1. Structural model of flying-wing aircraft and arrangement of sensors and actuators

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图 2 包含纯时滞模型及2~6阶Padé近似模型的舵机阶跃和频率响应

Figure 2. Step and frequency responses of actuator with pure time-delay model and 2~6 order Padé approximation models

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图 3 增稳控制系统结构

Figure 3. Stability augment control system

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图 4 阵风减缓主动控制系统

Figure 4. Gust alleviation active control system

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图 5 阵风减缓主动控制系统仿真模型

Figure 5. Simulation model of gust alleviation active control system

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图 6 舵机的仿真模型

Figure 6. Simulation model of actuator

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图 7 气动伺服弹性模型的阵风响应

Figure 7. Gust responses of aeroservoelastic model

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图 8 降阶前后控制系统的频率响应

Figure 8. Frequency responses of control system before and after order reduction

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图 9 降阶前后系统回差矩阵的最小奇异值

Figure 9. Minimum singular value of closed-loop system before and after order reduction

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表 1 阵风响应的均方根及减缓效果

Table 1. Root-mean-square of gust responses and effects of gust alleviation

均方根	3号加速度计处过载/g	4号加速度计处过载/g	翼根弯矩/ (N·m)
开环响应	0.071 2	0.071 7	2.294 8
闭环响应	0.058 1	0.062 3	1.645 8
减缓效率/%	18.39	13.11	28.28

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表 2 线性模型和非线性模型的阵风减缓效果

Table 2. Gust alleviation effects of linear model and nonlinear model

阵风响应	减缓效率/%
阵风响应	线性模型	非线性模型
3号加速度计处过载	18.40	18.39
4号加速度计处过载	13.16	13.11
翼根弯矩	28.30	28.28

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表 3 不同Padé近似阶数下所设计控制系统的阵风减缓效果

Table 3. Gust alleviation effects of designed control system based on different Padé approximation orders

近似阶数	减缓效率/%
近似阶数	3号加速度计处过载	4号加速度计处过载	翼根弯矩
2	8.57	-0.28	29.73
4	19.24	13.95	29.46
6	19.66	14.64	27.67
8	19.38	14.37	28.86
10	19.38	14.37	28.39

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表 4 控制律降阶对阵风减缓效果的影响

Table 4. Effect of order-reduction on gust alleviation

降阶阶数	减缓效率/%
降阶阶数	3号加速度计处过载	4号加速度计处过载	翼根弯矩
12	—	—	—
14	18.39	13.10	28.28
16	18.40	13.11	28.76
44	19.24	13.95	29.46
注：—表示不稳定。

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表 5 6阶Padé近似情况下控制律降阶对阵风减缓效果的影响

Table 5. Effect of order-reduction on gust alleviation in case of 6-order Padé approximation

降阶阶数	减缓效率/%
降阶阶数	3号加速度计处过载	4号加速度计处过载	翼根弯矩
12	7.56	0.50	24.13
14	11.25	5.43	24.72
16	19.31	14.22	27.22
50	19.66	14.64	27.67

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表 6 8阶Padé近似情况下控制律降阶对阵风减缓效果的影响

Table 6. Effect of order-reduction on gust alleviation in case of 8-order Padé approximation

降阶阶数	减缓效率/%
降阶阶数	3号加速度计处过载	4号加速度计处过载	翼根弯矩
12	7.37	12.00	25.04
14	10.70	4.35	26.09
16	19.31	14.06	28.22
56	19.38	14.37	28.86

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